Area of a Parallelogram Lesson Plan

Warm-up

The warm-up will be an essential part of this lesson to help introduce students to finding the area of a parallelogram.

Students will have various different ways of describing these two figures. Capture all the vocabulary words that they use. Some might wonder what the markings on the side mean. Some might misuse the vocabulary words. This warm-up will give you a good sense of students’ current understanding of parallelograms.

Understanding parallelograms

Introduce the name of this new shape: parallelograms. I find it normally helps to informally explain a parallelogram as a “slanted rectangle”. Since this is students’ first experience with parallelograms, you’ll want to explain the key features. The key features you’ll want to bring up include:

• Opposite sides are parallel and congruent, just like a rectangle.
• Base and height are perpendicular, just like a rectangle. 
• All rectangles are parallelograms.

Informal strategies for finding the area of the parallelogram

Because the parallelogram on the right shows the grid within the figure, students may have different approaches to finding the area of the parallelogram. Giving students time to think about their own approaches and encourage students to share their ideas with each other. Some students will find the area by counting how many of the boxes are cut in half so they can try to make whole boxes. Then they count how many boxes there would be in all. While the previous method does work, there will likely be some students who recognize that the left side of the parallelogram could be moved to create a rectangle. Then, they just have to find the area of the rectangle by counting the length and width.

Formalizing the formula for area of a parallelogram

As you listen to student conversations, try to note which students use the method of rearranging the parallelogram. Then, when reviewing as a class, make sure at least one of these students is able to share their method and why it works. This is an essential part of the lesson because it allows students to see how a parallelogram can become a rectangle. It also helps connect the formula for the area of a rectangle to the area of a parallelogram. One great way to transition is to ask students if we can still use a formula like “Area `=` length `\times`  width” if the figure is not a rectangle. This is a great opportunity for you to introduce the vocabulary of “base” and “height” for the parallelogram, and some students may even be able to guess what the different words should be.

Share this slide with students so that they can copy it for reference.

Identifying the base and height

Students should try to fill in the blanks if they are able to. It is important that students understand the base is always a side of the parallelogram. Students should also understand that the height always makes a right angle with the base. Keep in mind that the focus of this slide is to help students understand how to identify the base and height in order to help them find the area of a parallelogram. 

Examples for identifying base and height

For each figure, see if students can identify which value is the base and which value is the height. You could have students vote by raising their hands or giving a thumbs up for each number that is possible. When reviewing their answers, it may be helpful to pose some additional questions to them, such as:

• On the blue figure, how would you know what the base was if the `5` was on the top?
• On the red figure, what is one reason you know `9` cannot be the base?
• What is the area of each figure? 
• Which figure has a larger area?

Examples as a class

The next three examples are important for helping students practice finding the area of a parallelogram. The first example requires students to identify the base and height before calculating the area, the second is a rotated parallelogram with decimals, and in the third, they are given a verbal description. 

Start with this simpler example where the orientation of the parallelogram is the way a student would expect. Have students identify the base and height first, then multiply to find the area. 

This next example gets a bit trickier for students, since it has a different orientation. Help students to identify the base and height by reminding them that the base is always a side length of the parallelogram. You may also need to help students through the calculations with decimals. 

To further practice with decimals, students can try this problem on their own or with a partner. Again, students will need to be careful of their decimals. Some students may find this problem easier because the information is given to them directly; however, it gives the students an opportunity to see how to find the area of a parallelogram even if an image is not given.